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Question: a pharmaceutical product drug is sterilized by passing through a...

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A pharmaceutical product (drug) is sterilized by passing through a 10m long tube with diameter 12.7mm. The drug, flowing at a speed of 0.2m/s enters the tube at 25C and exits at 75C. The heating is affected by application of a uniform heat-flux. The drug properties are density = 1000kg/m3, Cp=4kJ/kg-K, mew = 2(10-3)kg/s-m, k=0.48W/m-K, and Pr = 10. The flow enters the tube fully developed hydraulically, but with uniform temperature profile (i.e., not thermally fully developed).

a) What is the required heat-transfer . (Ans. 12,682W/m2)

b) What is the tube surface temperature at the tube exit? (Ans. 152C)

c) What is the tube surface temperature at location x=0.5m ? Hint: Estimate the Nusselt number via Figure 8.10 (Incropera and Dewitt) in the thermally-developing region for constant heat-flux.

20 100 Thermal entry length Combined entry length 121 O Pr 0.7 Combined entry length (Pr 0.7) O Pr 2 40 10 Constant surface heat flux Equation 8.58 10 4.36 3.66 Constant surface temperature Equation 8.57 3.66 or numerator of 8.58 Entrance Fully developed Entrance Fully region developed region 0.001 0.01 0.1 0.5 1. 0.001 0.01 0.1 0.005 0.05 0.05 XID XID (a) FIGURE 8.10 Results obtained from entry length solutions for laminar flow in a circular tube with constant surface temperature: (a) Local Nusselt numbers. (b) Average Nusselt numbers

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